

A164003


Decimal expansion of exp(Pi^2/2).


1



0, 0, 7, 1, 9, 1, 8, 8, 3, 3, 5, 5, 8, 2, 6, 3, 6, 5, 6, 0, 7, 8, 0, 1, 3, 6, 6, 3, 9, 6, 3, 7, 1, 2, 0, 2, 9, 5, 5, 3, 6, 2, 3, 1, 8, 0, 8, 1, 5, 9, 7, 9, 4, 7, 5, 5, 8, 0, 3, 7, 1, 8, 1, 2, 4, 1, 2, 1, 3, 1, 8, 8, 6, 9, 7, 5, 6, 6, 5, 0, 8, 9, 5, 9, 6, 1, 0, 7, 9, 4, 3, 9, 8, 6, 5, 6, 6, 2, 3, 3, 0
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OFFSET

0,3


COMMENTS

Arises in connection with the expansion (e i)^(Pi i) = e^(Pi i) * i^(Pi i) = 1 * exp(Pi i log i) = exp(Pi i * Pi/2 i) = exp(Pi^2/2) = 0.00719188335582636560780136639...
One has to be careful about branches of multivalued complex functions. By definition (e i)^(Pi i) is exp(Pi i log(e i)) [using any of the branches of log] = exp(Pi i (1 + Pi i/2 + 2 n Pi i)) [ for any integer n ] =  exp( Pi^2/2  2 n Pi^2). There is no imaginary part in any of its branches. If n=0 we get (1) times the present constant.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000


EXAMPLE

.0071918833558263656078013663963712029553623180815979475580371...


MATHEMATICA

Join[{0, 0}, RealDigits[Exp[Pi^2/2], 10, 120][[1]]] (* Harvey P. Dale, Jul 11 2011 *)


PROG

(PARI) exp(Pi^2/2) \\ Charles R Greathouse IV, Mar 25 2014


CROSSREFS

Sequence in context: A019661 A200130 A284151 * A280704 A069609 A019855
Adjacent sequences: A164000 A164001 A164002 * A164004 A164005 A164006


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane, Aug 06 2010, based on postings to the Sequence Fans Mailing List by Alonso Del Arte, Charles R Greathouse IV, Sean A. Irvine, Robert Israel and other correspondents.


STATUS

approved



